The Laplacian spectrum of neural networks

Integrative, segregative, and degenerate harmonics of the structural connectome

Unifying integration and segregation in the brain has been a fundamental puzzle in neuroscience ever since the conception of the "binding problem." Here, we introduce a framework that places integration and segregation within a continuum based on a fundamental property of the brain-its structural connectivity graph Laplacian harmonics and a new feature we term the gap-spectrum. This framework organizes harmonics into three regimes-integrative, segregative, and degenerate-that together account for various group-level properties. Integrative and segregative harmonics occupy the ends of the continuum, and they share properties such as reproducibility across individuals, stability to perturbation, and involve "bottom-up" sensory networks. Degenerate harmonics are in the middle of the continuum, and they are subject-specific, flexible, and involve "top-down" networks. The proposed framework accommodates inter-subject variation, sensitivity to changes, and structure-function coupling in ways that offer promising avenues for studying cognition and consciousness in the brain.

Quantifying synergy and redundancy between networks

Understanding how different networks relate to each other is key for understanding complex systems. We introduce an intuitive yet powerful framework to disentangle different ways in which networks can be (dis)similar and complementary to each other. We decompose the shortest paths between nodes as uniquely contributed by one source network, or redundantly by either, or synergistically by both together. Our approach considers the networks' full topology, providing insights at multiple levels of resolution: from global statistics to individual paths. Our framework is widely applicable across scientific domains, from public transport to brain networks. In humans and 124 other species, we demonstrate the prevalence of unique contributions by long-range white-matter fibers in structural brain networks. Across species, efficient communication also relies on significantly greater synergy between long-range and short-range fibers than expected by chance. Our framework could find applications for designing network systems or evaluating existing ones.

A Comprehensive Survey on Community Detection With Deep Learning

Detecting a community in a network is a matter of discerning the distinct features and connections of a group of members that are different from those in other communities. The ability to do this is of great significance in network analysis. However, beyond the classic spectral clustering and statistical inference methods, there have been significant developments with deep learning techniques for community detection in recent years-particularly when it comes to handling high-dimensional network data. Hence, a comprehensive review of the latest progress in community detection through deep learning is timely. To frame the survey, we have devised a new taxonomy covering different state-of-the-art methods, including deep learning models based on deep neural networks (DNNs), deep nonnegative matrix factorization, and deep sparse filtering. The main category, i.e., DNNs, is further divided into convolutional networks, graph attention networks, generative adversarial networks, and autoencoders. The popular benchmark datasets, evaluation metrics, and open-source implementations to address experimentation settings are also summarized. This is followed by a discussion on the practical applications of community detection in various domains. The survey concludes with suggestions of challenging topics that would make for fruitful future research directions in this fast-growing deep learning field.

Does the brain behave like a (complex) network? I. Dynamics

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.

Brain network communication: concepts, models and applications

Understanding communication and information processing in nervous systems is a central goal of neuroscience. Over the past two decades, advances in connectomics and network neuroscience have opened new avenues for investigating polysynaptic communication in complex brain networks. Recent work has brought into question the mainstay assumption that connectome signalling occurs exclusively via shortest paths, resulting in a sprawling constellation of alternative network communication models. This Review surveys the latest developments in models of brain network communication. We begin by drawing a conceptual link between the mathematics of graph theory and biological aspects of neural signalling such as transmission delays and metabolic cost. We organize key network communication models and measures into a taxonomy, aimed at helping researchers navigate the growing number of concepts and methods in the literature. The taxonomy highlights the pros, cons and interpretations of different conceptualizations of connectome signalling. We showcase the utility of network communication models as a flexible, interpretable and tractable framework to study brain function by reviewing prominent applications in basic, cognitive and clinical neurosciences. Finally, we provide recommendations to guide the future development, application and validation of network communication models.

Spectral density-based clustering algorithms for complex networks

Introduction

Clustering is usually the first exploratory analysis step in empirical data. When the data set comprises graphs, the most common approaches focus on clustering its vertices. In this work, we are interested in grouping networks with similar connectivity structures together instead of grouping vertices of the graph. We could apply this approach to functional brain networks (FBNs) for identifying subgroups of people presenting similar functional connectivity, such as studying a mental disorder. The main problem is that real-world networks present natural fluctuations, which we should consider.

Methods

In this context, spectral density is an exciting feature because graphs generated by different models present distinct spectral densities, thus presenting different connectivity structures. We introduce two clustering methods: k-means for graphs of the same size and gCEM, a model-based approach for graphs of different sizes. We evaluated their performance in toy models. Finally, we applied them to FBNs of monkeys under anesthesia and a dataset of chemical compounds.

Results

We show that our methods work well in both toy models and real-world data. They present good results for clustering graphs presenting different connectivity structures even when they present the same number of edges, vertices, and degree of centrality.

Discussion

We recommend using k-means-based clustering for graphs when graphs present the same number of vertices and the gCEM method when graphs present a different number of vertices.

Connectome topology of mammalian brains and its relationship to taxonomy and phylogeny

Network models of anatomical connections allow for the extraction of quantitative features describing brain organization, and their comparison across brains from different species. Such comparisons can inform our understanding of between-species differences in brain architecture and can be compared to existing taxonomies and phylogenies. Here we performed a quantitative comparative analysis using the MaMI database (Tel Aviv University), a collection of brain networks reconstructed from ex vivo diffusion MRI spanning 125 species and 12 taxonomic orders or superorders. We used a broad range of metrics to measure between-mammal distances and compare these estimates to the separation of species as derived from taxonomy and phylogeny. We found that within-taxonomy order network distances are significantly closer than between-taxonomy network distances, and this relation holds for several measures of network distance. Furthermore, to estimate the evolutionary divergence between species, we obtained phylogenetic distances across 10,000 plausible phylogenetic trees. The anatomical network distances were rank-correlated with phylogenetic distances 10,000 times, creating a distribution of coefficients that demonstrate significantly positive correlations between network and phylogenetic distances. Collectively, these analyses demonstrate species-level organization across scales and informational sources: we relate brain networks distances, derived from MRI, with evolutionary distances, derived from genotyping data.

A connectomics-based taxonomy of mammals

Mammalian taxonomies are conventionally defined by morphological traits and genetics. How species differ in terms of neural circuits and whether inter-species differences in neural circuit organization conform to these taxonomies is unknown. The main obstacle to the comparison of neural architectures has been differences in network reconstruction techniques, yielding species-specific connectomes that are not directly comparable to one another. Here, we comprehensively chart connectome organization across the mammalian phylogenetic spectrum using a common reconstruction protocol. We analyse the mammalian MRI (MaMI) data set, a database that encompasses high-resolution ex vivo structural and diffusion MRI scans of 124 species across 12 taxonomic orders and 5 superorders, collected using a unified MRI protocol. We assess similarity between species connectomes using two methods: similarity of Laplacian eigenspectra and similarity of multiscale topological features. We find greater inter-species similarities among species within the same taxonomic order, suggesting that connectome organization reflects established taxonomic relationships defined by morphology and genetics. While all connectomes retain hallmark global features and relative proportions of connection classes, inter-species variation is driven by local regional connectivity profiles. By encoding connectomes into a common frame of reference, these findings establish a foundation for investigating how neural circuits change over phylogeny, forging a link from genes to circuits to behaviour.

Dyconnmap: Dynamic connectome mapping-A neuroimaging python module

Despite recent progress in the analysis of neuroimaging data sets, our comprehension of the main mechanisms and principles which govern human brain cognition and function remains incomplete. Network neuroscience makes substantial efforts to manipulate these challenges and provide real answers. For the last decade, researchers have been modelling brain structure and function via a graph or network that comprises brain regions that are either anatomically connected via tracts or functionally via a more extensive repertoire of functional associations. Network neuroscience is a relatively new multidisciplinary scientific avenue of the study of complex systems by pursuing novel ways to analyze, map, store and model the essential elements and their interactions in complex neurobiological systems, particularly the human brain, the most complex system in nature. Due to a rapid expansion of neuroimaging data sets' size and complexity, it is essential to propose and adopt new empirical tools to track dynamic patterns between neurons and brain areas and create comprehensive maps. In recent years, there is a rapid growth of scientific interest in moving functional neuroimaging analysis beyond simplified group or time‐averaged approaches and sophisticated algorithms that can capture the time‐varying properties of functional connectivity. We describe algorithms and network metrics that can capture the dynamic evolution of functional connectivity under this perspective. We adopt the word ‘chronnectome’ (integration of the Greek word ‘Chronos’, which means time, and connectome) to describe this specific branch of network neuroscience that explores how mutually informed brain activity correlates across time and brain space in a functional way. We also describe how good temporal mining of temporally evolved dynamic functional networks could give rise to the detection of specific brain states over which our brain evolved. This characteristic supports our complex human mind. The temporal evolution of these brain states and well‐known network metrics could give rise to new analytic trends. Functional brain networks could also increase the multi‐faced nature of the dynamic networks revealing complementary information. Finally, we describe a python module (https://github.com/makism/dyconnmap) which accompanies this article and contains a collection of dynamic complex network analytics and measures and demonstrates its great promise for the study of a healthy subject's repeated fMRI scans.

Multiparametric EEG analysis of brain network dynamics during neonatal seizures

BACKGROUND

One of the most challenging issues in paediatric neurology is the diagnosis of neonatal seizures, whose delayed treatment may affect the neurodevelopment of the newborn. Formulation of the correct diagnosis is conditioned by the high number of perceptually or automatically detected false positives.

NEW METHOD

New methodologies are proposed to assess neonatal seizures trend over time. Our approach is based on the analysis of standardized trends of two properties of the brain network: the Synchronizabilty (S) and the degree of phase synchronicity given by the Circular Omega Complexity (COC). Qualitative and quantitative methods based on network dynamics allow differentiating seizure events from interictal periods and seizure-free patients.

RESULTS

The methods were tested on a public dataset of labelled neonatal seizures. COC shows significant differences among seizure and non-seizure events (p-value <0.001, Cohen's d 0.86). Combining S and COC in standardized temporal instants provided a reliable description of the physiological behaviour of the brain's network during neonatal seizures.

COMPARISON WITH EXISTING METHOD(S)

Few of the existing network methods propose an operative way for carrying their analytical approach into the diagnostic process of neonatal seizures. Our methods offer a simple representation of brain network dynamics easily implementable and understandable also by less experienced staff.

CONCLUSIONS

Our findings confirm the usefulness of the evaluation of brain network dynamics over time for a better understanding and interpretation of the complex mechanisms behind neonatal seizures. The proposed methods could also reliably support existing seizure detectors as a post-processing step in doubtful cases.

Asymmetric high-order anatomical brain connectivity sculpts effective connectivity

Bridging the gap between symmetric, direct white matter brain connectivity and neural dynamics that are often asymmetric and polysynaptic may offer insights into brain architecture, but this remains an unresolved challenge in neuroscience. Here, we used the graph Laplacian matrix to simulate symmetric and asymmetric high-order diffusion processes akin to particles spreading through white matter pathways. The simulated indirect structural connectivity outperformed direct as well as absent anatomical information in sculpting effective connectivity, a measure of causal and directed brain dynamics. Crucially, an asymmetric diffusion process determined by the sensitivity of the network nodes to their afferents best predicted effective connectivity. The outcome is consistent with brain regions adapting to maintain their sensitivity to inputs within a dynamic range. Asymmetric network communication models offer a promising perspective for understanding the relationship between structural and functional brain connectomes, both in normalcy and neuropsychiatric conditions.

Brain network similarity: methods and applications

Graph theoretical approach has proved an effective tool to understand, characterize, and quantify the complex brain network. However, much less attention has been paid to methods that quantitatively compare two graphs, a crucial issue in the context of brain networks. Comparing brain networks is indeed mandatory in several network neuroscience applications. Here, we discuss the current state of the art, challenges, and a collection of analysis tools that have been developed in recent years to compare brain networks. We first introduce the graph similarity problem in brain network application. We then describe the methodological background of the available metrics and algorithms of comparing graphs, their strengths, and limitations. We also report results obtained in concrete applications from normal brain networks. More precisely, we show the potential use of brain network similarity to build a "network of networks" that may give new insights into the object categorization in the human brain. Additionally, we discuss future directions in terms of network similarity methods and applications.

Metrics for graph comparison: A practitioner's guide

Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees yield insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies at different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and real world networks. We put forward a multi-scale picture of graph structure wherein we study the effect of global and local structures on changes in distance measures. We make recommendations on the applicability of different distance measures to the analysis of empirical graph data based on this multi-scale view. Finally, we introduce the Python library NetComp that implements the graph distances used in this work.

Relating network connectivity to dynamics: opportunities and challenges for theoretical neuroscience

We review recent work relating network connectivity to the dynamics of neural activity. While concepts stemming from network science provide a valuable starting point, the interpretation of graph-theoretic structures and measures can be highly dependent on the dynamics associated to the network. Properties that are quite meaningful for linear dynamics, such as random walk and network flow models, may be of limited relevance in the neuroscience setting. Theoretical and computational neuroscience are playing a vital role in understanding the relationship between network connectivity and the nonlinear dynamics associated to neural networks.

Spectral peculiarity and criticality of a human connectome

We have performed the comparative spectral analysis of structural connectomes for various organisms using open-access data. Our results indicate new peculiar features of connectomes of higher organisms. We found that the spectral density of adjacency matrices of human connectome has maximal deviation from the one of randomized network, compared to other organisms. Considering the network evolution induced by the preference of 3-cycles formation, we discovered that for macaque and human connectomes the evolution with the conservation of local clusterization is crucial, while for primitive organisms the conservation of averaged clusterization is sufficient. Investigating for the first time the level spacing distribution of the spectrum of human connectome Laplacian matrix, we explicitly demonstrate that the spectral statistics corresponds to the critical regime, which is hybrid of Wigner-Dyson and Poisson distributions. This observation provides strong support for debated statement of the brain criticality.

Guided graph spectral embedding: Application to the C. elegans connectome

Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions—for example, based on wavelets and Slepians—that can be applied to filter signals defined on the graph. In this work, we take inspiration from these constructions to define a new guided spectral embedding that combines maximizing energy concentration with minimizing modified embedded distance for a given importance weighting of the nodes. We show that these optimization goals are intrinsically opposite, leading to a well-defined and stable spectral decomposition. The importance weighting allows us to put the focus on particular nodes and tune the trade-off between global and local effects. Following the derivation of our new optimization criterion, we exemplify the methodology on the C. elegans structural connectome. The results of our analyses confirm known observations on the nematode’s neural network in terms of functionality and importance of cells. Compared with Laplacian embedding, the guided approach, focused on a certain class of cells (sensory neurons, interneurons, or motoneurons), provides more biological insights, such as the distinction between somatic positions of cells, and their involvement in low- or high-order processing functions.

Connectome Smoothing via Low-Rank Approximations

In brain imaging and connectomics, the study of brain networks, estimating the mean of a population of graphs based on a sample is a core problem. Often, this problem is especially difficult because the sample or cohort size is relatively small, sometimes even a single subject, while the number of nodes can be very large with noisy estimates of connectivity. While the element-wise sample mean of the adjacency matrices is a common approach, this method does not exploit the underlying structural properties of the graphs. We propose using a low-rank method that incorporates dimension selection and diagonal augmentation to smooth the estimates and improve performance over the naïve methodology for small sample sizes. Theoretical results for the stochastic block model show that this method offers major improvements when there are many vertices. Similarly, we demonstrate that the low-rank methods outperform the standard sample mean for a variety of independent edge distributions as well as human connectome data derived from the magnetic resonance imaging, especially when the sample sizes are small. Moreover, the low-rank methods yield "eigen-connectomes," which correlate with the lobe-structure of the human brain and superstructures of the mouse brain. These results indicate that the low-rank methods are the important parts of the toolbox for researchers studying populations of graphs in general and statistical connectomics in particular.

Thermodynamics of network model fitting with spectral entropies

An information-theoretic approach inspired by quantum statistical mechanics was recently proposed as a means to optimize network models and to assess their likelihood against synthetic and real-world networks. Importantly, this method does not rely on specific topological features or network descriptors but leverages entropy-based measures of network distance. Entertaining the analogy with thermodynamics, we provide a physical interpretation of model hyperparameters and propose analytical procedures for their estimate. These results enable the practical application of this novel and powerful framework to network model inference. We demonstrate this method in synthetic networks endowed with a modular structure and in real-world brain connectivity networks.

Voting Simulation based Agglomerative Hierarchical Method for Network Community Detection

Community detection has been paid much attention in many fields in recent years, and a great deal of community-detection methods have been proposed. But the time consumption of some of them is heavy, limiting them from being applied to large-scale networks. On the contrary, there exist some lower-time-complexity methods. But most of them are non-deterministic, meaning that running the same method many times may yield different results from the same network, which reduces their practical utility greatly in real-world applications. To solve these problems, we propose a community-detection method in this paper, which takes both the quality of the results and the efficiency of the detecting procedure into account. Moreover, it is a deterministic method which can extract definite community structures from networks. The proposed method is inspired by the voting behaviours in election activities in the social society, in which we first simulate the voting procedure on the network. Every vertex votes for the nominated candidates following the proposed voting principles, densely connected groups of vertices can quickly reach a consensus on their candidates. At the end of this procedure, candidates and their own voters form a group of clusters. Then, we take the clusters as initial communities, and agglomerate some of them into larger ones with high efficiency to obtain the resulting community structures. We conducted extensive experiments on some artificial networks and real-world networks, the experimental results show that our proposed method can efficiently extract high-quality community structures from networks, and outperform the comparison algorithms significantly.

Brain network eigenmodes provide a robust and compact representation of the structural connectome in health and disease

Recent research has demonstrated the use of the structural connectome as a powerful tool to characterize the network architecture of the brain and potentially generate biomarkers for neurologic and psychiatric disorders. In particular, the anatomic embedding of the edges of the cerebral graph have been postulated to elucidate the relative importance of white matter tracts to the overall network connectivity, explaining the varying effects of localized white matter pathology on cognition and behavior. Here, we demonstrate the use of a linear diffusion model to quantify the impact of these perturbations on brain connectivity. We show that the eigenmodes governing the dynamics of this model are strongly conserved between healthy subjects regardless of cortical and sub-cortical parcellations, but show significant, interpretable deviations in improperly developed brains. More specifically, we investigated the effect of agenesis of the corpus callosum (AgCC), one of the most common brain malformations to identify differences in the effect of virtual corpus callosotomies and the neurodevelopmental disorder itself. These findings, including the strong correspondence between regions of highest importance from graph eigenmodes of network diffusion and nexus regions of white matter from edge density imaging, show converging evidence toward understanding the relationship between white matter anatomy and the structural connectome.

While the structural connectome of the brain has emerged as a powerful tool towards understanding the progression of neurologic and psychiatric disorders, links between the anatomy of connections within the brain and the effects of localized white matter pathology on cognition are still an active area of investigation. Here, we propose the use of the diffusion process towards understanding perturbations of brain connectivity. We find that while the dynamics of this process are strongly conserved in healthy subjects, they display significant, interpretable deviations in agenesis of the corpus callosum, one of the most common brain malformations. These findings, including the strong similarity between regions identified to be crucial towards diffusion and nexus regions of white matter from edge density imaging, show converging evidence towards understanding the relationship between white matter anatomy and the structural connectome.

Childhood maltreatment is associated with alteration in global network fiber-tract architecture independent of history of depression and anxiety

Childhood maltreatment is a major risk factor for psychopathology. It is also associated with alterations in the network architecture of the brain, which we hypothesized may play a significant role in the development of psychopathology. In this study, we analyzed the global network architecture of physically healthy unmedicated 18-25 year old subjects (n=262) using diffusion tensor imaging (DTI) MRI and tractography. Anatomical networks were constructed from fiber streams interconnecting 90 cortical or subcortical regions for subjects with no-to-low (n=122) versus moderate-to-high (n=140) exposure to maltreatment. Graph theory analysis revealed lower degree, strength, global efficiency, and maximum Laplacian spectra, higher pathlength, small-worldness and Laplacian skewness, and less deviation from artificial networks in subjects with moderate-to-high exposure to maltreatment. On balance, local clustering was similar in both groups, but the different clusters were more strongly interconnected in the no-to-low exposure group. History of major depression, anxiety and attention deficit hyperactivity disorder did not have a significant impact on global network measures over and above the effect of maltreatment. Maltreatment is an important factor that needs to be taken into account in studies examining the relationship between network differences and psychopathology.

Super-Spreader Identification Using Meta-Centrality

Super-spreaders are the nodes of a network that can maximize their impacts on other nodes, e.g., in the case of information spreading or virus propagation. Many centrality measures have been proposed to identify such nodes from a given network. However, it has been observed that the identification accuracy based on those measures is not always satisfactory among different types of networks. In addition, the nodes identified by using single centrality are not always placed in the top section, where the super-spreaders are supposed to be, of the ranking generated by simulation. In this paper we take a meta-centrality approach by combining different centrality measures using a modified version of Borda count aggregation method. As a result, we are able to improve the performance of super-spreader identification for a broad range of real-world networks. While doing so, we discover a pattern in the centrality measures involved in the aggregation with respect to the topological structures of the networks used in the experiments. Further, we study the eigenvalues of the Laplacian matrix, also known as Laplacian spectrum, and by using the Earth Mover’s distance as a metric for the spectrum, we are able to identify four clusters to explain the aggregation results.

Topological organization of connectivity strength in the rat connectome

The mammalian brain is a complex network of anatomically interconnected regions. Animal studies allow for an invasive measurement of the connections of these networks at the macroscale level by means of neuronal tracing of axonal projections, providing a unique opportunity for the formation of detailed 'connectome maps'. Here we analyzed the macroscale connectome of the rat brain, including detailed information on the macroscale interregional pathways between 67 cortical and subcortical regions as provided by the high-quality, open-access BAMS-II database on rat brain anatomical projections, focusing in particular on the non-uniform distribution of projection strength across pathways. First, network analysis confirmed a small-world, modular and rich club organization of the rat connectome; findings in clear support of previous studies on connectome organization in other mammalian species. More importantly, analyzing network properties of different connection weight classes, we extend previous observations by showing that pathways with different topological roles have significantly different levels of connectivity strength. Among other findings, intramodular connections are shown to display a higher connectivity strength than intermodular connections and hub-to-hub rich club connections are shown to include significantly stronger pathways than connections spanning between peripheral nodes. Furthermore, we show evidence indicating that edges of different weight classes display different topological structures, potentially suggesting varying roles and origins of pathways in the mammalian brain network.

Comparative Connectomics

We introduce comparative connectomics, the quantitative study of cross-species commonalities and variations in brain network topology that aims to discover general principles of network architecture of nervous systems and the identification of species-specific features of brain connectivity. By comparing connectomes derived from simple to more advanced species, we identify two conserved themes of wiring: the tendency to organize network topology into communities that serve specialized functionality and the general drive to enable high topological integration by means of investment of neural resources in short communication paths, hubs, and rich clubs. Within the space of wiring possibilities that conform to these common principles, we argue that differences in connectome organization between closely related species support adaptations in cognition and behavior.

The Neonatal Connectome During Preterm Brain Development

The human connectome is the result of an elaborate developmental trajectory. Acquiring diffusion-weighted imaging and resting-state fMRI, we studied connectome formation during the preterm phase of macroscopic connectome genesis. In total, 27 neonates were scanned at week 30 and/or week 40 gestational age (GA). Examining the architecture of the neonatal anatomical brain network revealed a clear presence of a small-world modular organization before term birth. Analysis of neonatal functional connectivity (FC) showed the early formation of resting-state networks, suggesting that functional networks are present in the preterm brain, albeit being in an immature state. Moreover, structural and FC patterns of the neonatal brain network showed strong overlap with connectome architecture of the adult brain (85 and 81%, respectively). Analysis of brain development between week 30 and week 40 GA revealed clear developmental effects in neonatal connectome architecture, including a significant increase in white matter microstructure (P < 0.01), small-world topology (P < 0.01) and interhemispheric FC (P < 0.01). Computational analysis further showed that developmental changes involved an increase in integration capacity of the connectivity network as a whole. Taken together, we conclude that hallmark organizational structures of the human connectome are present before term birth and subject to early development.

Do Brain Networks Evolve by Maximizing Their Information Flow Capacity?

We propose a working hypothesis supported by numerical simulations that brain networks evolve based on the principle of the maximization of their internal information flow capacity. We find that synchronous behavior and capacity of information flow of the evolved networks reproduce well the same behaviors observed in the brain dynamical networks of Caenorhabditis elegans and humans, networks of Hindmarsh-Rose neurons with graphs given by these brain networks. We make a strong case to verify our hypothesis by showing that the neural networks with the closest graph distance to the brain networks of Caenorhabditis elegans and humans are the Hindmarsh-Rose neural networks evolved with coupling strengths that maximize information flow capacity. Surprisingly, we find that global neural synchronization levels decrease during brain evolution, reflecting on an underlying global no Hebbian-like evolution process, which is driven by no Hebbian-like learning behaviors for some of the clusters during evolution, and Hebbian-like learning rules for clusters where neurons increase their synchronization.

Altered amygdalar resting-state connectivity in depression is explained by both genes and environment

Recent findings indicate that alterations of the amygdalar resting-state fMRI connectivity play an important role in the etiology of depression. While both depression and resting-state brain activity are shaped by genes and environment, the relative contribution of genetic and environmental factors mediating the relationship between amygdalar resting-state connectivity and depression remain largely unexplored. Likewise, novel neuroimaging research indicates that different mathematical representations of resting-state fMRI activity patterns are able to embed distinct information relevant to brain health and disease. The present study analyzed the influence of genes and environment on amygdalar resting-state fMRI connectivity, in relation to depression risk. High-resolution resting-state fMRI scans were analyzed to estimate functional connectivity patterns in a sample of 48 twins (24 monozygotic pairs) informative for depressive psychopathology (6 concordant, 8 discordant and 10 healthy control pairs). A graph-theoretical framework was employed to construct brain networks using two methods: (i) the conventional approach of filtered BOLD fMRI time-series and (ii) analytic components of this fMRI activity. Results using both methods indicate that depression risk is increased by environmental factors altering amygdalar connectivity. When analyzing the analytic components of the BOLD fMRI time-series, genetic factors altering the amygdala neural activity at rest show an important contribution to depression risk. Overall, these findings show that both genes and environment modify different patterns the amygdala resting-state connectivity to increase depression risk. The genetic relationship between amygdalar connectivity and depression may be better elicited by examining analytic components of the brain resting-state BOLD fMRI signals.

The Budapest Reference Connectome Server v2.0

The connectomes of different human brains are pairwise distinct: we cannot talk about an abstract "graph of the brain". Two typical connectomes, however, have quite a few common graph edges that may describe the same connections between the same cortical areas. The Budapest Reference Connectome Server v2.0 generates the common edges of the connectomes of 96 distinct cortexes, each with 1015 vertices, computed from 96 MRI data sets of the Human Connectome Project. The user may set numerous parameters for the identification and filtering of common edges, and the graphs are downloadable in both csv and GraphML formats; both formats carry the anatomical annotations of the vertices, generated by the FreeSurfer program. The resulting consensus graph is also automatically visualized in a 3D rotating brain model on the website. The consensus graphs, generated with various parameter settings, can be used as reference connectomes based on different, independent MRI images, therefore they may serve as reduced-error, low-noise, robust graph representations of the human brain. The webserver is available at http://connectome.pitgroup.org.

Linking macroscale graph analytical organization to microscale neuroarchitectonics in the macaque connectome

Macroscale connectivity of the mammalian brain has been shown to display several characteristics of an efficient communication network architecture. In parallel, at the microscopic scale, histological studies have extensively revealed large interregional variation in cortical neural architectonics. However, how these two "scales" of cerebrum organization are linked remains an open question. Collating and combining data across multiple studies on the cortical cytoarchitecture of the macaque cortex with information on macroscale anatomical wiring derived from tract tracing studies, this study focuses on examining the interplay between macroscale organization of the macaque connectome and microscale cortical neuronal architecture. Our findings show that both macroscale degree as well as the topological role in the overall network are related to the level of neuronal complexity of cortical regions at the microscale, showing (among several effects) a positive overall association between macroscale degree and metrics of microscale pyramidal complexity. Macroscale hub regions, together forming a densely interconnected "rich club," are noted to display a high level of neuronal complexity, findings supportive of a high level of integrative neuronal processes to occur in these regions. Together, we report on cross-scale observations that jointly suggest that a region's microscale neuronal architecture is tuned to its role in the global brain network.

Chasing the dreams of early connectionists

Mapping and examining the wiring pattern of neural systems is a fundamental pillar of neuroscience. In this Viewpoint, we review a recently described mesoscale connectome map of the mouse brain. We underscore the map's high spatial resolution and discuss key organizational network attributes of the presented connectome, its potential impact on neuroscience, and the general importance of connectome maps to obtain insight in the workings of the brain at a system's level.

Brain networks in schizophrenia

Schizophrenia--a severe psychiatric condition characterized by hallucinations, delusions, loss of initiative and cognitive function--is hypothesized to result from abnormal anatomical neural connectivity and a consequent decoupling of the brain's integrative thought processes. The rise of in vivo neuroimaging techniques has refueled the formulation of dysconnectivity hypotheses, linking schizophrenia to abnormal structural and functional connectivity in the brain at both microscopic and macroscopic levels. Over the past few years, advances in high-field structural and functional neuroimaging techniques have made it increasingly feasible to reconstruct comprehensive maps of the macroscopic neural wiring system of the human brain, know as the connectome. In parallel, advances in network science and graph theory have improved our ability to study the spatial and topological organizational layout of such neural connectivity maps in detail. Combined, the field of neural connectomics has created a novel platform that provides a deeper understanding of the overall organization of brain wiring, its relation to healthy brain function and human cognition, and conversely, how brain disorders such as schizophrenia arise from abnormal brain network wiring and dynamics. In this review we discuss recent findings of connectomic studies in schizophrenia that examine how the disorder relates to disruptions of brain connectivity.